Roy is stuck repeating the same comfortable, placid suburban day every day while living in Irvine, California. Irvine is notorious for being a comfortable, placid, homogeneous community.
Everyone is surprised when Nyles reveals that Tala donated bone marrow to her brother Niko, and her father even asks, "How did he know that?" because she kept it so secret. Sarah told him. Presumably during a prior loop, she complained to Nyles about how her perfect sister is so saintly that she donated bone marrow and didn't even brag, giving Nyles the inspiration for his wedding toast in a later loop.
Sarah does seem the most likely source of information. When we see Nyles interact with pre-loop Sarah their conversation does convey the feeling that she's tired of always being considered the black sheep of the family and one can see the exchange proposed above occuring. However, ultimately, it's just speculation because the story doesn't say that this was a tightly held secret, just that Howard was puzzled how Nyles knew and he could have picked it up from conversations he had with Nico or any other member of the Wilder family in his decades of looping.
It's not definitive, but upon a rewatch the intention does seem to be foreshadowing that Nyles is lying to Sarah about never having slept with her before — the Chekhov's Gun about knowing what brand of hair mist she's wearing (because it's a gift she got from Tala that she feels obligated to wear on her wedding) is something almost nobody else at the wedding would've or could've told him about but her.
Why did Nyles go into the desert at night instead of staying at the party? We know he was there getting a drink at the bar in his tux late into the day. Perhaps he walked in on Misty cheating, was upset and went for a walk to escape and stumbled on the cave.
"The pain is real" seems to be Nyles' primary guiding principle: avoiding pain and seeking pleasure being the only things that he thinks matter. But it turns out that pain is a crucial driving force for all three of them. For Roy, dying slowly in an ICU is what finally causes him to give up his pointless quest for revenge and appreciate have unlimited time to spend with his family. For Sarah, the emotional pain of her breakup with Nyles (and finally facing her guilt about Abe) drives her to do whatever it takes to escape from the loop. For Nyles himself, the pain of losing Sarah causes him to realize that he'd rather take a risk than be stuck in the loop forever without her.
As shown in the mid-credits scene, Nyles is still present in the loop after his (and Sarah's) attempt to escape. On the surface, that does not seem to be a problem, because this version of him is not aware of being in a loop (he has become a "NPC" like the other wedding guests). However, this also means that he will repeat his actions of his first wedding night, and be trapped in the time loop again. That would explain why Nana seems to know that Sarah is leaving the loop ("I'll guess you'll be going now. Good luck."): Nana is probably also stuck in the loop and this is not the first time she has seen Sarah leaving. Best case scenario: Nana finally decides to leave the loop, and makes sure no one is trapped in the loop before leaving.
Sarah spends what would have to be years teaching herself quantum physics and bomb making. Under normal circumstances, this would be quite difficult. In the loop, she has no way of taking notes in class or tracking her progress, which would have significantly slowed her down.
In order for anyone to end up trapped in the time loop in the first place, they'd have to be the kind of person who would impulsively go spelunking in an earthquake-prone area of the open desert on the night of a wedding. There's a certain amount of Anthropic Principle involved in guaranteeing the primary person in the time loop is a Manchild for whom the loop is a metaphor for his own irresponsibility.
The movie showed that the earthquake that opened the cave occurred in the late morning or afternoon BEFORE the wedding not the evening plus the cave was within walking distance of the hotel. This allows for plenty of time for a curious, reasonable person to explore it. The film also shows that the cave entrance was pretty wide open and one didn't need to enter very far before being caught by the time loop, so it didn't require an impulsive, irresponsible attitude willing to explore dangerous conditions to get trapped especially since the movie suggests that Nana might also be a participant in the time loop.
The movie reveals what actually happens when someone escapes the loop in the mid-credits sequence — anyone still trapped in the loop will find them replaced with the pre-loop version of themselves who never experienced it. Notably, this contradicts what Sarah says happened when she tested her escape plan on Spuds' goat — she says the goat physically vanished, but when Roy goes looking for Nyles after the ending Nyles is still there, just with no memory of meeting him. This could be a plot hole, or... Sarah was lying when she said Spuds' goat disappeared and proved her theory was correct. Spuds' goat, like Nyles and Sarah, had its mind reverted to its original state while its soul went onward to inhabit the Nov. 10th version of itself in the real world — and Sarah realized this must have been what happened but, the goat being a goat and unable to communicate, also realized she had no way of proving it. So she lied to Nyles to get him off his ass, hence the dialogue in the ending where Nyles asks Sarah to reassure him about the test and she tells him it's a Leap of Faith.
What you've described is most likely plot hole, but given the looping mechanics the story provides, there is a way for Sarah to determine if her hypothesis was valid. During her testing montage we see that she first brings Spud's goat with her into the cave thus creating a looped-version of the goat. If, before she did that she marked the goat in some way (branded, notched an ear, colored it with a sharpie,etc) then the looped-version goat would now retain that mark on each loop. When she "later" sent the goat loaded with C-4 into the cave and blew it up, that marked version would have been knocked out of the loop and replaced by the pre-loop and unmarked version of the goat. So when Sarah starts her own new loop and goes to Spud's farm and sees the unmarked goat, she knows the marked goat has "disappeared" or physically vanished but had no way of knowing where it went. So what she said to Nyles was true "from a certain point of view".
That might be the explanation the filmmakers wanted to go with but it's pretty strongly contradicted by the fact that the human loopers can only be changed psychologically by the loops, not physically — Nyles and Sarah have both died violently multiple times and carry no signs of injury into future loops, Sarah lampshades that of course she "looks good" because she "can't age", there's a scene of Nyles and Sarah giving each other Embarrassing Tattoos with the knowledge they'll just disappear, etc. This includes physical changes caused on the day of the first loop — Sarah starts the loop by walking into the cave wearing her bridesmaid's gown, only to wake up in the clothes she was dressed in that morning. So the only way for Sarah to know whether her test subject was "still the same goat" would be based on the goat's memories, which would be kind of hard to test, given that after all it's just a goat.
Good point. My thought was that the state of the physical body (not the clothes) you entered the loop resets with each loop. So tattoos/injuries you gain during the day vanish but tattoos/injuries you already had remain. But if it's something non-corporal like a "quantum essence" (or soul or spirit or whatever) that traverses the loop and lands in a fresh, new quantum body each reset, then, yeah, only memories, personality, thoughts would persist. In that case, there'd be nothing to indicate to Sarah that anything changed about the goat and the stinger implies that the goat wouldn't just disappear. Sadly, this would make her entire experiment pointless.
You can actually train a goat if she visited the goat everyday for months worth of time it'd recognize her and she could teach a single simple command. After her experiment the goat she knew was gone and this "new goat" no longer recognizes her or understands the trick she taught it. Even putting that aside, without the interference of a looper the goat would repeat the exact same actions every day. Put the goat into the loop and it will act a little different each day. She blew up the goat and the replacement goat is back to repeating the same routine.
This latter explanation — that Sarah can tell it's "not the same goat anymore" but can't prove it — works the best with the situation in the movie, where Sarah does have a good reason from her own POV to think that her plan will work but for Nyles not checking to see if the goat is still there makes his decision a leap of faith.
It's also possible that the day that Roy decided to go to the wedding to see about Sarah's theory was a different day from when Sarah and Nyles left the time loop. So on the day they left they would have disappeared like the goat, but on subsequent days they would be reverted back to their pre-loop selves from Roy's perspective.
Now that all three of the now-free loppies know how to escape, down to the second, they could conceivably enter and exit the loop whenever they whim takes them. While they won’t have a wedding to make things more interesting, they’ve basically discovered the best vacation destination in the world; a place where you can’t die and suffer no long-term consequences for anything you do. And when the novelty wears off, you can leave with no further issues.
Technically, yes. However, we don't know whether Nyles and Sarah's escape "broke" or "weakened" the quantum tunnel so that Roy's attempt to escape could fail or whether repeated C4 explosions in the tunnel will eventually cause it to collapse and kill the person trying to escape. It comes down to whether it's worth the risk to have a "vacation spot" that could eventually collapse and trap you forever or kill you when you try to escape and you're a few seconds off your timing when you detonate the C4.
